Effects of density-dependent dispersal behaviours on the speed and spatial patterns of range expansion in predator–prey metapopulations

Dispersal can strongly affect the spatiotemporal dynamics of a species (its spread, spatial distribution and persistence). We investigated how two dispersal behaviours, namely prey evasion (PE) and predator pursuit (PP), affect the dynamics of a predator–prey system. PE portrays the tendency of prey avoiding predators by dispersing into adjacent patches with fewer predators, while PP describes the tendency of predators to pursue the prey by moving into patches with more prey. Based on the Beddington predation model, a spatially explicit metapopulation model was built to incorporate PE and PP. Numerical simulations were run to investigate the effects of PE and PP on the rate of spread, spatial synchrony and the persistence of populations. Results show that both PE and PP can alter spatial synchrony although PP has a weaker desynchronising effect than PE. The predator–prey system without PE and PP expanded in circular waves. The effect of PE can push the prey to distribute in a circular ring front, whereas the effect of PP can change the circular waves to anisotropic expansion. Furthermore, weak PE and PP can accelerate the spread of prey while strong and disproportionate intensities slow down the range expansion. The effects of PE and PP further enhance the population size, break down the spatial synchrony and promote the persistence of populations.